1. **State the problem:** We need to find the slope of the line passing through the points $(-2, -2)$ and $(1, 3)$ and determine if the slope is positive or negative. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula represents the "rise over run," meaning the change in $y$ divided by the change in $x$. 3. **Calculate the slope:** Substitute the points: $$m = \frac{3 - (-2)}{1 - (-2)} = \frac{3 + 2}{1 + 2} = \frac{5}{3}$$ 4. **Simplify and interpret:** The slope is $\frac{5}{3}$, which is positive because both numerator and denominator are positive. 5. **Conclusion:** The slope is positive, so the correct answer is (a) positive. **Final answer:** $$\boxed{\text{slope} = \frac{5}{3}, \text{positive}}$$